1. **State the problem:** Find the mean of the data set: 10, 13, 11, 16, 21, 19, 15, 10, 16, 18, 19, 13, 13, 17, 17. 2. **Recall the formula for the mean:** $$\text{Mean} = \frac{\text{Sum of all data values}}{\text{Number of data values}}$$ 3. **Calculate the sum of the data values:** $$10 + 13 + 11 + 16 + 21 + 19 + 15 + 10 + 16 + 18 + 19 + 13 + 13 + 17 + 17 = 244$$ 4. **Count the number of data values:** There are 15 numbers in the data set. 5. **Calculate the mean:** $$\text{Mean} = \frac{244}{15}$$ 6. **Simplify the fraction:** $$\text{Mean} = \frac{\cancel{244}}{\cancel{15}} = 16.27$$ (rounded to two decimal places) 7. **Final answer:** The mean of the data set is approximately $16.27$.